If a variable line is moving such that the intercepts made by it on the coordinate axes are reciprocal to each other,then the points $P(x, y)$ on such lines satisfy

Ten ants are on the real line. At time $t=0$,the $k$-th ant starts at the point $k^2$ and,travelling at a uniform speed,reaches the point $(11-k)^2$ at time $t=1$. The number of distinct times at which at least two ants are at the same location is

The locus of the midpoint of the portion of the line $x \cos \alpha + y \sin \alpha = p$ intercepted by the coordinate axes,where $p$ is a constant,is

$A$ straight line passing through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points $P$ and $Q$. If $O$ is the origin and the rectangle $OPRQ$ is completed,then the locus of $R$ is:

$A$ point moves in the $XY$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $3$. The area enclosed by the locus of that point is (in sq. units)

If non-zero numbers $a, b, c$ are in harmonic progression,then the straight line $\frac{x}{a} + \frac{y}{b} + \frac{1}{c} = 0$ always passes through a fixed point. Find the coordinates of that point.